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Sindrei [870]
3 years ago
11

Step by step factoring: x^2-11xy+30y^2

Mathematics
1 answer:
oee [108]3 years ago
5 0
Do you need it explained or just the answer

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In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank
fredd [130]

Answer:

1) Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) Amount \ of \, water \ remaining \ in \, the \ tank \ is \  \frac{x^3(6-\pi) }{6}

Step-by-step explanation:

1) Here we have;

First tank A

Volume of tank = x³

The  volume of the sphere = \frac{4}{3} \pi r^3

However, the diameter of the sphere = x therefore;

r = x/2 and the volume of the sphere is thus;

volume of the sphere = \frac{4}{3} \pi \frac{x^3}{8}= \frac{1}{6} \pi x^3

For tank B

Volume of tank = x³

The  volume of the spheres = 8 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 2·D = x therefore;

r = x/4 and the volume of the sphere is thus;

volume of the spheres = 8 \times \frac{4}{3} \pi (\frac{x}{4})^3= \frac{x^3 \times \pi }{6}

For tank C

Volume of tank = x³

The  volume of the spheres = 64 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 4·D = x therefore;

r = x/8 and the volume of the sphere is thus;

volume of the spheres = 64 \times \frac{4}{3} \pi (\frac{x}{8})^3= \frac{x^3 \times \pi }{6}

Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) For the 4th tank, we have;

number of spheres on side of the tank, n is given thus;

n³ = 512

∴ n = ∛512 = 8

Hence we have;

Volume of tank = x³

The  volume of the spheres = 512 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 8·D = x therefore;

r = x/16 and the volume of the sphere is thus;

volume of the spheres = 512\times \frac{4}{3} \pi (\frac{x}{16})^3= \frac{x^3 \times \pi }{6}

Amount of water remaining in the tank is given by the following expression;

Amount of water remaining in the tank = Volume of tank - volume of spheres

Amount of water remaining in the tank = x^3 - \frac{x^3 \times \pi }{6} = \frac{x^3(6-\pi) }{6}

Amount \ of \ water \, remaining \, in \, the \ tank =  \frac{x^3(6-\pi) }{6}.

5 0
3 years ago
Help pls!!!
SVEN [57.7K]

Answer:

an = -6n + 5.

Step-by-step explanation:

This is an arithmetic sequence with first term a1 = -1 and common difference d = -6

an = a1 + d(n-1)

an = -1 + -6(n - 1)

an = -1 -6n + 6

an = -6n + 5.

3 0
3 years ago
HELP ME QUICK PLEASE THIS IS A TEST OMG
xxMikexx [17]

Answer:

It's 1/2,-2 just did the math.

3 0
2 years ago
HELP FIRST GETS BRAINLY
TiliK225 [7]

Answer:

3/21 most simplest form is 1/7

Step-by-step explanation:

4 0
3 years ago
62 strings of orange lights and 22 strings of yellow lights were used in the house each string of lights has 36 bulbs how many b
Allisa [31]

62 + 22 = 84 total light strings.

36 bulbs/string multiplied by 84 light strings = 3,024 total light bulbs

5 0
3 years ago
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